Their isn't really a difference between the American Revolution and the War of Independence. The "War of independence" is another form of writing the "American Revolution."
The only difference I see that an independence was a part of a country that split from the dependent one while a revolution is in a war of independence, but doesn't always result in a independence. A revolution could occur in that one country alone without a war at all.
This war was fought between the 13 colonies and the UK.
First battle fought in Lexington and Concord.
Last battle fought in Yorktown.
After lots of fighting the 13 colonies pulled through and gained independence on July 4, 1776.
